There is a consensus based on conclusions made in IRS memorandum 201201017 (2012) that allows tax payers to use any reasonable method to determine the amount of deductible interest.
In my opinion, a reasonable way when a main home is sold and a new main home is purchased in the same year is to amortize the average balance over 12 months. Pick one of your purchased homes as your new main home. For the sold main home and new main home loan total up monthly balances for Jan through Dec, with 0 for the months the loan was not held. Also zero out the balance and interest for one of these homes in the months the loans overlap. Total up the balances and divide by 12. This is a reasonable average balance for your 'main home' during the year. Add this to the average balance of your other purchased home, your 'second home' during the year.
However, since your sold home was only held for the first two month of the year, it would be simpler to just declare the home as not secured in Turbo Tax. Should get the same result.
Note: You can use the interest paid divided by the interest rate when the mortgage is held for less than 12 months if you divide the result by the percentage of months it was held.
